CN107179758B - Dynamic signal parameter identification method and system - Google Patents

Dynamic signal parameter identification method and system Download PDF

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CN107179758B
CN107179758B CN201710365432.6A CN201710365432A CN107179758B CN 107179758 B CN107179758 B CN 107179758B CN 201710365432 A CN201710365432 A CN 201710365432A CN 107179758 B CN107179758 B CN 107179758B
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envelope
parameters
curve
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value
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CN107179758A (en
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姜春阳
周峰
张淮清
谢岩
彭涛
魏胜清
殷小东
熊博
余也凤
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State Grid Corp of China SGCC
China Electric Power Research Institute Co Ltd CEPRI
State Grid Tianjin Electric Power Co Ltd
State Grid Hubei Electric Power Co Ltd
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State Grid Corp of China SGCC
China Electric Power Research Institute Co Ltd CEPRI
State Grid Tianjin Electric Power Co Ltd
State Grid Hubei Electric Power Co Ltd
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    • G05B19/41885—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS], computer integrated manufacturing [CIM] characterised by modeling, simulation of the manufacturing system
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Abstract

The invention discloses a method and a system for identifying dynamic signal parameters, wherein the method comprises the following steps: establishing a mathematical model of the current according to the shape of the envelope curve of the dynamic signal current waveform; judging the type of a mathematical model of the current according to the first derivative value and the second derivative value of the curve envelope point and the ratio of the second derivative value to the first derivative value; selecting a pre-estimation algorithm aiming at the judged mathematical model type of the current according to the judged mathematical model type of the current, and pre-estimating parameters of the envelope part and the direct current part by using the pre-estimation algorithm to obtain approximate values of the parameters of the envelope part and the direct current part; and identifying the envelope parameters by using a differential algorithm according to the approximate values of the envelope parameters to obtain accurate values of the envelope parameters and the direct current components. The method has good effect on the global optimization of the envelope parameters by adopting the differential evolution algorithm, and has higher convergence speed and higher precision.

Description

Dynamic signal parameter identification method and system
Technical Field
The present invention relates to the field of dynamic signal analysis, and more particularly, to a method and a system for identifying dynamic signal parameters.
Background
Dynamic signals are time-varying signals that can be divided into deterministic signals and random signals. If the signal is represented as a defined function of time, for a given moment, a corresponding function value can be determined, which signal is called deterministic or regular. The essence of which can be described by a determined mathematical relationship. While random signals cannot be described by accurate mathematical expression relations, the amplitude, frequency and phase at any moment cannot be predicted in advance, but the random signals have statistical rules and can be analyzed by a statistical method.
The signal is a carrier of information, and in actual industrial production, the dynamic signal contains information about various electric loads such as a steel mill, an electric locomotive, a forging machine and the like. The information often contains the running condition of the electric load, and abnormal working state can be revealed through analysis of the dynamic signal, so that a theoretical basis is provided for fault diagnosis. In recent years, nonlinear loads such as semiconductor devices are increasingly applied to power systems, which not only causes harmonic pollution to the power systems, but also affects accurate measurement of electric energy.
In the prior art, because a unified mathematical model for describing dynamic signals does not exist, not only can the characteristic quantity of the signals not be accurately extracted for analysis, but also the error of the existing electric energy metering method is often larger. Therefore, it is important to find a mathematical model more suitable for describing dynamic signals. Because the distortion rate of the voltage waveform is small in general, the difference of the characteristic quantities extracted from the voltage waveforms of different types of loads is not large.
Therefore, a technique is needed to accurately identify the dynamic signal parameters.
Disclosure of Invention
The invention provides a method and a system for identifying dynamic signal parameters, which aim to solve the problem of how to identify the dynamic signal parameters.
In order to solve the above problem, the present invention provides a method for identifying dynamic signal parameters, comprising:
establishing a mathematical model of the current according to the shape of the envelope curve of the dynamic signal current waveform;
judging the type of a mathematical model of the current according to the first derivative value and the second derivative value of the curve envelope point and the ratio of the second derivative value to the first derivative value;
selecting a pre-estimation algorithm aiming at the judged mathematical model type of the current according to the judged mathematical model type of the current, and pre-estimating parameters of an envelope part and a direct current part by using the pre-estimation algorithm to obtain approximate values of the parameters of the envelope part and the direct current part;
and identifying the envelope parameters by using a differential algorithm according to the approximate values of the envelope parameters to obtain accurate values of the envelope parameters and the direct current components.
Preferably, the mathematical model types are a diagonal envelope model, a parabolic envelope model and an exponential envelope model, respectively.
Preferably, the harmonic parameters of the power frequency part are estimated by using a Hanning window Hanning interpolation method.
Preferably, the establishing of the oblique line envelope model according to the harmonic parameters of the power frequency part is as follows:
Figure BDA0001301457220000021
in the formula (1), a and b are respectively the slope and constant of a sloping envelope curve h (t) approximately equal to (at + b), Am,fm,θmRespectively, power frequency partial amplitude, power frequency partial frequency and power frequency partial phase, B0The value of M is 11, and t is the sampling time corresponding to the dynamic signal;
the parabolic envelope model is:
Figure BDA0001301457220000022
in the formula (2), a, b and c are respectively parabola envelope curves h' (t) approximately equal to (at)2Coefficient of the quadratic term, coefficient of the first order term and constant, + bt + c), Am,fm,θmRespectively, power frequency partial amplitude, power frequency partial frequency and power frequency partial phase, B0The value of M is 11, and t is the sampling time corresponding to the dynamic signal;
the exponential envelope model is:
Figure BDA0001301457220000031
in the formula (3), a, b and c are respectively exponential envelope curves h' (t) ≈ aebt+ c) amplification factor, attenuation factor and constant, Am,fm,θmRespectively, power frequency partial amplitude, power frequency partial frequency and power frequency partial phase, B0And M is a direct current component, the value of M is 11, and t is the sampling time corresponding to the dynamic signal.
Preferably, the determining the type of the mathematical model of the current according to the first derivative value, the second derivative value and the ratio of the second derivative value to the first derivative value of the curve envelope point includes,
the mathematical model of the oblique line envelope curve is h (t) approximately equal to (at + b) (1-1),
in the formula (1-1), a and b are respectively a slope and a constant of a sloping envelope curve h (t) (at + b), and t is a sampling time corresponding to the dynamic signal;
calculating the slope of the curve envelope point:
Figure BDA0001301457220000032
in the formula (1-2), Δ t is any time interval, t1Any time in the sampling time period;
and if the calculated slope value of the envelope point of the envelope curve is a constant, judging that the type of the mathematical model of the current is a sloping line envelope model.
Preferably, the determining the type of the mathematical model of the current according to the first derivative value, the second derivative value and the ratio of the second derivative value to the first derivative value of the curve envelope point includes,
the mathematical model of the parabola envelope curve is h' (t) ≈ at2+bt+c) (2-1)，
In the formula (2-1), a, b and c are respectively parabola envelope curves h' (t) ≈ at2A quadratic term coefficient, a primary term coefficient and a constant of + bt + c), wherein t is the sampling time corresponding to the dynamic signal;
calculating a second order differential function value of a curve envelope point:
Figure BDA0001301457220000041
in the formula (2-2), Δ t is any time interval, t1Is any time in the sampling period;
and if the calculated second order differential function value of the envelope point of the envelope curve is constant, judging that the type of the mathematical model of the current is a parabolic envelope model.
Preferably, the determining the type of the mathematical model of the current according to the first derivative value, the second derivative value and the ratio of the second derivative value to the first derivative value of the curve envelope point includes,
if the ratio of the second derivative value of the curve enveloping point to the first derivative value of the enveloping point is constant, judging that the mathematical model type of the current is an exponential enveloping model:
the mathematical model of the exponential envelope curve is h' (t) ≈ aebt+c)(3-1)，
In the formula (3-1), a, b and c are respectively exponential envelope curves h' (t) ≈ aebt+ c) amplification factor, attenuation factor and constant.
Calculating the ratio of the second order differential to the first order differential of the envelope point:
Figure BDA0001301457220000042
Figure BDA0001301457220000051
in the formula (3-2), Δ t is any time interval, t1Is any time in the sampling period;
and if the ratio of the second derivative value of the curve enveloping point to the first derivative value of the enveloping point is constant, judging that the type of the mathematical model of the current is an exponential enveloping model.
Preferably, the estimating algorithm for the determined mathematical model type of the current is selected according to the determined mathematical model type of the current, and the estimating algorithm is used to estimate the parameters of the envelope part and the direct current part to obtain the approximate values of the parameters of the envelope part and the direct current part, wherein the estimating of the parameters of the oblique line envelope part and the direct current part is as follows:
dividing the sampling data points into time segments according to the selected sampling time interval delta t, screening out the maximum value in each time segment range, thereby obtaining the envelope point of the curve in the whole sampling time range, calculating the first derivative of the oblique line function of the envelope part, and estimating a, B and B0Approximation a of*、b*、B0 *Setting an envelopeThe curve is h (T) approximately equals (at + b), T is the power frequency period, T1For any time within the sampling period, the calculation formula is as follows:
(1)
Figure BDA0001301457220000052
(2)
Figure BDA0001301457220000053
(3)
Figure BDA0001301457220000054
in the formula (1-3), a and B are respectively the slope and constant of the oblique line envelope curve h (t) approximately equal to (at + B), and B0Is a direct current component; a is*、b*、B0 *Is a, B, B0An approximation of (d); Δ t is any time interval, t1Is any time in the sampling period; length (T) is the length of the data point at time T, and T is length (T).
Preferably, the estimation algorithm for the mathematical model type of the judged current is selected according to the judged mathematical model type of the current, and the parameters of the envelope part and the direct current part are estimated by using the estimation algorithm to obtain the approximate values of the parameters of the envelope part and the direct current part, wherein the estimation of the parameters of the parabolic envelope part and the direct current part is as follows:
dividing the sampling data points into time segments according to the selected sampling time interval delta t, screening out the maximum value in each time segment range, thereby obtaining the envelope point of the curve in the whole sampling time range, calculating the second derivative of the parabolic function of the envelope part, and estimating a, B, c, B0Approximation a of*、b*、c*、B0 *Let the envelope curve be h' (t) ≈ at2+ bt + c), T is power frequency period, T1At any time in the sampling period, the calculation formula is as follows:
(1)
Figure BDA0001301457220000061
(2)
Figure BDA0001301457220000062
(3)
Figure BDA0001301457220000063
(4)
Figure BDA0001301457220000064
in the formula (2-3), a, b and c are respectively parabola envelope curves h' (t) ≈ at2Coefficient of quadratic term, coefficient of primary term and constant, + bt + c), B0Is a direct current component; a is*、b*、c*、B0 *Is a, B, c, B0Is any time interval, t1Is any time in the sampling period; length (T) is the length of the data point at time T, and T is length (T).
Preferably, the estimating algorithm for the mathematical model type of the judged current is selected according to the judged mathematical model type of the current, and the estimating algorithm is used to estimate the parameters of the envelope part and the direct current part to obtain the approximate values of the parameters of the envelope part and the direct current part, wherein the estimating of the parameters of the exponential envelope part and the direct current part is as follows:
dividing the sampling data points into time segments according to the selected sampling time interval delta t, screening out the maximum value in each time segment range to obtain the envelope point of the curve in the whole sampling time range, calculating the ratio of the second derivative of the exponential function of the envelope part to the first-order layer number, and calculating a, B, c and B0Approximation a of*、b*、c*、B0 *Let the envelope curve be h' (t) ≈ aebt+ c), T is the power frequency period, T1For any time in the sampling period, the calculation formula is as follows:
(1)
Figure BDA0001301457220000071
(2)
Figure BDA0001301457220000072
(3)
Figure BDA0001301457220000073
(4)
Figure BDA0001301457220000074
in the formula (3-3), a, b and c are respectively exponential envelope curves h' (t) ≈ aebt+ c) amplification factor, attenuation factor and constant, B0Is a direct current component; a is*、b*、c*、B0 *Is a, B, c, B0An estimate of (d); Δ t is any time interval, t1Is any time in the sampling period; length (T) is the length of the data point at time T, and T is length (T).
Preferably, the envelope parameters are identified by using a difference algorithm according to the approximate values of the envelope parameters, and accurate values of the envelope parameters and the direct current components are obtained, wherein the accurate values of the parameters of the oblique line envelope part and the direct current part are calculated as follows:
according to a parameter approximation a of the envelope part*、b*、c*、B0 *Calculating the range of iteration initial value, and identifying the parameters a, B, c and B of the envelope part by using a differential evolution algorithm0The exact value of (2) is to construct a diagonal envelope objective function as follows:
Figure BDA0001301457220000081
in the formula (1-4), a and b are respectively the slope and constant of the oblique line envelope curve h (t) approximately equal to (at + b), Am,fm,θmAmplitude, frequency and phase, respectively, of the power frequency part, B0For the DC component, gc (t) is the actual data sample point, length (t) is the data point length at time t, and M takes the value of 11;
setting the problem to be optimized as
Figure BDA0001301457220000082
(x) is the target function of the slope envelope, the steps of the differential evolution algorithm are described as follows:
(2) the initialization is carried out in such a way that,
inputting evolution parameters: population size m (40 ≦ m ≦ 60), chromosome length, that is, the number of objective function arguments, crossover probability C0.98, crossover factor F0.4, evolution algebra d (1 ≦ d ≦ 500), and lower bound x of N argumentsmin＝0.5·(a*、b*、c*、B0 *) And an upper bound xmax＝1.5·(a*、b*、c*、B0 *) Randomly generating an initial population matrix
Figure BDA0001301457220000083
Where each row represents an individual of the population and each column represents the gene of that individual. Each element of the initial population matrix is generated as follows:
xmn＝xmin(n)+rand(0,1)·(xmax(n)-xmin(n))，
in the above formula, rand (0,1) is a random number generated between (0, 1).
(3) The variation is carried out on the basis of the variation,
for each individual x in the populationmnGenerating three random integers r1,r2,r3∈{1,2,…,N},r1≠r2≠r3And a random integer jrandE.g. 1,2, …, N, generating variant individual zmn：
Figure BDA0001301457220000084
(6) The cross-over is carried out,
current individual xmnAnd variant individuals zmnCross to obtain competitive individual umn：
Figure BDA0001301457220000091
(7) Selecting
Calculating competitive individuals umnTarget value f (u)mn) To obtain a selected individual kmn：
Figure BDA0001301457220000092
(8) The verification is terminated and the verification is terminated,
if f (k)mn) D is not more than 0.1or 500, k is outputmnAs the optimal solution. Otherwise, put xmn＝kmnAnd d +1, and turning to the mutation step (2).
Preferably, the envelope parameters are identified by using a difference algorithm according to the approximate values of the envelope parameters, and accurate values of the envelope parameters and the direct current component are obtained, wherein the accurate values of the parameters of the parabolic envelope part and the direct current part are calculated as follows:
according to a parameter approximation a of the envelope part*、b*、c*、B0 *Calculating the range of iteration initial value, and identifying the parameters a, B, c and B of the envelope part by using a differential evolution algorithm0The parabolic envelope objective function is constructed as follows:
Figure BDA0001301457220000093
in the formula (2-4), a, b and c are respectively parabola envelope curves h' (t) ≈ at2Coefficient of the quadratic term, coefficient of the first order term and constant, + bt + c), Am,fm,θmAmplitude, frequency and phase, respectively, of the power frequency part, B0The direct current component gc (t) is an actual data sampling point, the length (t) is a data point length of time t, and the value of M is 11;
setting the problem to be optimized as
Figure BDA0001301457220000094
(x) is a parabolic envelope objective function, then the steps of the differential evolution algorithm are described as follows:
(1) the initialization is carried out in such a way that,
inputting evolution parameters: population size m (40 ≦ m ≦ 60), chromosome length, that is, the number of objective function arguments, crossover probability C0.98, crossover factor F0.4, evolution algebra d (1 ≦ d ≦ 500), and lower bound x of N argumentsmin＝0.5·(a*、b*、c*、B0 *) And an upper bound xmax＝1.5·(a*、b*、c*、B0 *) Randomly generating an initial population matrix
Figure BDA0001301457220000101
Where each row represents an individual of the population and each column represents the gene of that individual. Each element of the initial population matrix is generated as follows:
xmn＝xmin(n)+rand(0,1)·(xmax(n)-xmin(n))，
in the above formula, rand (0,1) is a random number generated between (0, 1).
(2) The variation is carried out on the basis of the variation,
for each individual x in the populationmnGenerating three random integers r1,r2,r3∈{1,2,…,N},r1≠r2≠r3And a random integer jrandE.g. 1,2, …, N, generating variant individual zmn：
Figure BDA0001301457220000102
(3) The cross-over is carried out,
current individual xmnAnd variant individuals zmnCross to obtain competitive individual umn：
Figure BDA0001301457220000103
(4) Selecting
Calculating competitive individuals umnTarget value f (u)mn) To obtain a selected individual kmn：
Figure BDA0001301457220000104
(5) The verification is terminated and the verification is terminated,
if f (k)mn) D is not more than 0.1or 500, k is outputmnAs the optimal solution. Otherwise, put xmn＝kmnAnd d +1, and turning to the mutation step (2).
Preferably, the envelope parameters are identified by using a difference algorithm according to the approximate values of the envelope parameters, and accurate values of the envelope parameters and the direct current components are obtained, wherein the accurate values of the parameters of the exponential envelope part and the direct current part are calculated as follows:
according to a parameter approximation a of the envelope part*、b*、c*、B0 *Calculating the range of iteration initial value, and identifying the parameters a, B, c and B of the envelope part by using a differential evolution algorithm0The parabolic envelope objective function is constructed as follows:
Figure BDA0001301457220000111
in the formula (3-4), a, b and c are respectively exponential envelope curves h' (t) ≈ aebt+ c) amplification factor, attenuation factor and constant, Am,fm,θmAmplitude, frequency and phase, respectively, of the power frequency part, B0The direct current component gc (t) is an actual data sampling point, the length (t) is a data point length of time t, and the value of M is 11;
setting the problem to be optimized as
Figure BDA0001301457220000112
(x) is an exponential envelope objective function, then the steps of the differential evolution algorithm are described as follows:
(1) the initialization is carried out in such a way that,
inputting evolution parameters: seed of a plantGroup size m, (40. ltoreq. m.ltoreq.60), chromosome length, that is, the number of objective function arguments, crossover probability C0.98, crossover factor F0.4, evolution algebra d, (1. ltoreq. d.ltoreq.500), and lower bound x of N argumentsmin＝0.5·(a*、b*、c*、B0 *) And an upper bound xmax＝1.5·(a*、b*、c*、B0 *) Randomly generating an initial population matrix
Figure BDA0001301457220000113
Where each row represents an individual of the population and each column represents the gene of that individual. Each element of the initial population matrix is generated as follows:
xmn＝xmin(n)+rand(0,1)·(xmax(n)-xmin(n))，
in the above formula, rand (0,1) is a random number generated between (0, 1).
(2) The variation is carried out on the basis of the variation,
for each individual x in the populationmnGenerating three random integers r1,r2,r3∈{1,2,…,N},r1≠r2≠r3And a random integer jrandE.g. 1,2, …, N, generating variant individual zmn：
Figure BDA0001301457220000121
(3) The cross-over is carried out,
current individual xmnAnd variant individuals zmnCross to obtain competitive individual umn：
Figure BDA0001301457220000122
(4) Selecting
Calculating competitive individuals umnTarget value f (u)mn) To obtain a selected individual kmn：
Figure BDA0001301457220000123
(5) The verification is terminated and the verification is terminated,
if f (k)mn) D is not more than 0.1or 500, k is outputmnAs the optimal solution. Otherwise, put xmn＝kmnAnd d +1, and turning to the mutation step (2).
Based on another aspect of the present invention, the present invention provides a dynamic signal parameter identification system, including:
the establishing unit is used for establishing a mathematical model of the current according to the envelope curve shape of the dynamic signal current waveform;
the initial unit judges the type of a mathematical model of the current according to the first order derivative value and the second order derivative value of the curve envelope point and the ratio of the second order derivative value to the first order derivative value;
the first calculation unit selects a pre-estimation algorithm aiming at the judged mathematical model type of the current according to the judged mathematical model type of the current, and pre-estimates the parameters of the envelope part and the direct current part by utilizing the pre-estimation algorithm to obtain approximate values of the parameters of the envelope part and the direct current part;
and the second calculating unit identifies the envelope parameters by using a differential algorithm according to the approximate values of the envelope parameters to obtain accurate values of the envelope parameters and the direct current components.
The technical scheme of the invention provides a more perfect mathematical model for describing the dynamic signal current, has better applicability, organically combines a windowing interpolation algorithm and an envelope parameter estimation algorithm, solves the envelope parameter, the direct current component and the attenuation factor in the model by using the envelope parameter estimation algorithm, and overcomes the limitation of the application of the windowing interpolation algorithm. The technical scheme of the invention has good effect on the global optimization of the envelope parameters by adopting the differential evolution algorithm, avoids the limitation of the common optimization algorithm, and has higher convergence speed and higher precision.
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A more complete understanding of exemplary embodiments of the present invention may be had by reference to the following drawings in which:
FIG. 1 is a flowchart illustrating a method for identifying dynamic signal parameters according to an embodiment of the present invention;
FIG. 2 is a graph of a dynamic signal ferro-electric current according to an embodiment of the present invention;
FIG. 3 is a graph of dynamic signal ramp envelope model current reconstruction according to an embodiment of the present invention;
FIG. 4 is a block diagram of a dynamic signal parameter identification system according to an embodiment of the present invention.
Detailed Description
The exemplary embodiments of the present invention will now be described with reference to the accompanying drawings, however, the present invention may be embodied in many different forms and is not limited to the embodiments described herein, which are provided for complete and complete disclosure of the present invention and to fully convey the scope of the present invention to those skilled in the art. The terminology used in the exemplary embodiments illustrated in the accompanying drawings is not intended to be limiting of the invention. In the drawings, the same units/elements are denoted by the same reference numerals.
Unless otherwise defined, terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Further, it will be understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense.
Fig. 1 is a flowchart illustrating a method for identifying dynamic signal parameters according to an embodiment of the invention. After the current model for scientifically describing the dynamic signals is established, the types of the load current models of various types are identified and distinguished so as to improve the accuracy and efficiency of electric energy metering. The method adopts a windowing interpolation algorithm to calculate harmonic parameters of a power frequency part, including the amplitude of the power frequency part, the frequency of the power frequency part and the phase of the power frequency part; the embodiment of the invention can accurately fit the real dynamic signal current waveform. In the embodiment of the invention, other parameters (direct current components, attenuation factors and the like) are calculated, an envelope parameter value estimation algorithm is adopted, the approximate value of the envelope parameter is firstly obtained, the approximate value is used as the initial range of the iteration of the differential evolution algorithm, and the accurate parameter values of the direct current components, the attenuation factors and the like are obtained by solving the objective function. As shown in fig. 1, the method 100 begins at step 101:
preferably, a mathematical model of the current is established in step 101 based on the shape of the envelope curve of the dynamic signal current waveform. In the embodiment of the invention, the mathematical model types are a diagonal envelope model, a parabolic envelope model and an exponential envelope model respectively.
Wherein, the oblique line envelope model is:
Figure BDA0001301457220000141
in the formula (1), a and b are respectively the slope and constant of a sloping envelope curve h (t) approximately equal to (at + b), Am,fm,θmRespectively, power frequency partial amplitude, power frequency partial frequency and power frequency partial phase, B0The value of M is 11, and t is the sampling time corresponding to the dynamic signal;
the parabolic envelope model is:
Figure BDA0001301457220000142
in the formula (2), a, b and c are respectively parabola envelope curves h' (t) approximately equal to (at)2Coefficient of the quadratic term, coefficient of the first order term and constant, + bt + c), Am,fm,θmRespectively, power frequency partial amplitude, power frequency partial frequency and power frequency partial phase, B0The value of M is 11, and t is the sampling time corresponding to the dynamic signal;
the exponential envelope model is:
Figure BDA0001301457220000151
in the formula (3), a, b and c are respectively exponential envelope curves h' (t) ≈ aebt+ c) amplification factor, attenuation factor and constant, Am,fm,θmRespectively, power frequency partial amplitude, power frequency partial frequency and power frequency partial phase, B0And M is a direct current component, the value of M is 11, and t is the sampling time corresponding to the dynamic signal.
Preferably, in step 102, the type of the mathematical model of the current is determined according to the first derivative value, the second derivative value and the ratio of the second derivative value to the first derivative value of the curve envelope point.
The method for judging the oblique line envelope model comprises the following steps:
the mathematical model of the oblique line envelope curve is set as h (t) approximately equal to (at + b) (1-1),
in the formula (1-1), a and b are respectively a slope and a constant of a sloping envelope curve h (t) (at + b), and t is a sampling time corresponding to the dynamic signal;
calculating the slope of the curve envelope point:
Figure BDA0001301457220000152
in the formula (1-2), Δ t is any time interval, t1Any time in the sampling time period;
and if the calculated slope value of the envelope point of the envelope curve is a constant, judging that the type of the mathematical model of the current is a sloping line envelope model.
The method for judging the mathematical model of the parabolic envelope curve comprises the following steps:
the mathematical model of the parabola envelope curve is h' (t) ≈ at2+bt+c)(2-1)，
In the formula (2-1), a, b and c are respectively parabola envelope curves h' (t) ≈ at2A quadratic term coefficient, a primary term coefficient and a constant of + bt + c), wherein t is the sampling time corresponding to the dynamic signal;
calculating a second order differential function value of a curve envelope point:
Figure BDA0001301457220000161
in the formula (2-2), Δ t is any time interval, t1Is any time in the sampling period;
and if the calculated second order differential function value of the envelope point of the envelope curve is constant, judging that the type of the mathematical model of the current is a parabolic envelope model.
The judgment method of the exponential envelope model comprises the following steps:
the mathematical model of the exponential envelope curve is h' (t) ≈ aebt+c)(3-1)，
In the formula (3-1), a, b and c are respectively exponential envelope curves h' (t) ≈ aebt+ c) amplification factor, attenuation factor and constant.
Calculating the ratio of the second order differential to the first order differential of the envelope point:
Figure BDA0001301457220000162
in the formula (3-2), Δ t is any time interval, t1Is any time in the sampling period;
and if the ratio of the second derivative value of the curve enveloping point to the first derivative value of the enveloping point is constant, judging that the type of the mathematical model of the current is an exponential enveloping model.
Preferably, the harmonic parameters of the power frequency part are estimated by using Hanning window interpolation method. In the embodiment of the invention, the harmonic parameters of the power frequency part comprise the amplitude of the power frequency part, the frequency of the power frequency part and the phase of the power frequency part.
Preferably, in step 103, a prediction algorithm for the determined mathematical model type of the current is selected according to the determined mathematical model type of the current, and parameters of the envelope part and the direct current part are predicted by using the prediction algorithm to obtain approximate values of the parameters of the envelope part and the direct current part.
The parameters of the oblique line enveloping part and the direct current part are estimated as follows:
time-dividing the sampled data points according to the selected sampling time interval delta tSegmenting, screening out the maximum value in each time segmentation range to obtain the envelope point of the curve in the whole sampling time range, calculating the first derivative of the oblique line function of the envelope part, and estimating a, B and B0Approximation a of*、b*、B0 *Let the envelope curve be h (T) approximately equal to (at + b), T be the power frequency period, T1For any time within the sampling period, the calculation formula is as follows:
(1)
Figure BDA0001301457220000171
(2)
Figure BDA0001301457220000172
(3)
Figure BDA0001301457220000173
in the formula (1-3), a and B are respectively the slope and constant of the oblique line envelope curve h (t) approximately equal to (at + B), and B0Is a direct current component; a is*、b*、B0 *Is a, B, B0An approximation of (d); Δ t is any time interval, t1Is any time in the sampling period; length (T) is the length of the data point at time T, and T is length (T).
Wherein, the parameters of the parabola envelope part and the DC part are estimated as follows:
dividing the sampling data points into time segments according to the selected sampling time interval delta t, screening out the maximum value in each time segment range, thereby obtaining the envelope point of the curve in the whole sampling time range, calculating the second derivative of the parabolic function of the envelope part, and estimating a, B, c, B0Approximation a of*、b*、c*、B0 *Let the envelope curve be h' (t) ≈ at2+ bt + c), T is power frequency period, T1At any time in the sampling period, the calculation formula is as follows:
(1)
Figure BDA0001301457220000181
(2)
Figure BDA0001301457220000182
(3)
Figure BDA0001301457220000183
(4)
Figure BDA0001301457220000184
in the formula (2-3), a, b and c are respectively parabola envelope curves h' (t) ≈ at2Coefficient of quadratic term, coefficient of primary term and constant, + bt + c), B0Is a direct current component; a is*、b*、c*、B0 *Is a, B, c, B0Is any time interval, t1Is any time in the sampling period; length (T) is the length of the data point at time T, and T is length (T).
The parameters of the exponential envelope part and the direct current part are estimated as follows:
dividing the sampling data points into time segments according to the selected sampling time interval delta t, screening out the maximum value in each time segment range to obtain the envelope point of the curve in the whole sampling time range, calculating the ratio of the second derivative of the exponential function of the envelope part to the first-order layer number, and calculating a, B, c and B0Approximation a of*、b*、c*、B0 *Let the envelope curve be h' (t) ≈ aebt+ c), T is the power frequency period, T1For any time in the sampling period, the calculation formula is as follows:
(1)
Figure BDA0001301457220000191
(2)
Figure BDA0001301457220000192
(3)
Figure BDA0001301457220000193
(4)
Figure BDA0001301457220000194
in the formula (3-3), a, b and c are respectively exponential envelope curves h' (t) ≈ aebt+ c) amplification factor, attenuation factor and constant, B0Is a direct current component; a is*、b*、c*、B0 *Is a, B, c, B0An estimate of (d); Δ t is any time interval, t1Is any time in the sampling period; length (T) is the length of the data point at time T, and T is length (T).
Preferably, in step 104, the envelope parameters are identified by using a difference algorithm according to the approximate values of the envelope parameters, and accurate values of the envelope parameters and the direct current components are obtained.
The accurate parameter values for calculating the oblique line envelope part and the direct current part are as follows:
approximation of a parameter based on the envelope part*、b*、c*、B0 *Calculating the range of iteration initial value, and identifying the parameters a, B, c and B of the envelope part by using a differential evolution algorithm0The exact value of (2) is to construct a diagonal envelope objective function as follows:
Figure BDA0001301457220000195
in the formula (1-4), a and b are respectively the slope and constant of the oblique line envelope curve h (t) approximately equal to (at + b), Am,fm,θmAmplitude, frequency and phase, respectively, of the power frequency part, B0Is a direct current component, gc (t) is an actual data sampling point, length (t) is a data point length of time t, and the value of M is 11;
setting the problem to be optimized as
Figure BDA0001301457220000201
f (x) isIf the target function is enveloped by oblique lines, the steps of the differential evolution algorithm are described as follows:
(1) the initialization is carried out in such a way that,
inputting evolution parameters: population size m, (40 ≦ m ≦ 60), chromosome length, i.e., number N of objective function independent variables, crossover probability C ≦ 0.98, crossover factor F ≦ 0.4, evolution algebra d, (1 ≦ d ≦ 500), lower bound x of independent variablesmin＝0.5·(a*、b*、c*、B0 *) And an upper bound xmax＝1.5·(a*、b*、c*、B0 *) Randomly generating an initial population matrix
Figure BDA0001301457220000202
Where each row represents an individual of the population and each column represents the gene of that individual. Each element of the initial population matrix is generated as follows:
xmn＝xmin(n)+rand(0,1)·(xmax(n)-xmin(n))，
in the above formula, rand (0,1) is a random number generated between (0, 1).
(2) The variation is carried out on the basis of the variation,
for each individual x in the populationmnGenerating three random integers r1,r2,r3∈{1,2,…,N},r1≠r2≠r3And a random integer jrandE.g. 1,2, …, N, generating variant individual zmn：
Figure BDA0001301457220000203
(3) The cross-over is carried out,
current individual xmnAnd variant individuals zmnCross to obtain competitive individual umn：
Figure BDA0001301457220000204
(4) Selecting
Calculating competitive individuals umnTarget value f (u)mn) To obtain a selected individual kmn：
Figure BDA0001301457220000211
(5) The verification is terminated and the verification is terminated,
if f (k)mn) D is not more than 0.1or 500, k is outputmnAs the optimal solution. Otherwise, put xmn＝kmnAnd d +1, and turning to the mutation step (2).
The accurate parameter values for calculating the parabolic envelope part and the direct current part are as follows:
approximation of a parameter based on the envelope part*、b*、c*、B0 *Calculating the range of iteration initial value, and identifying the parameters a, B, c and B of the envelope part by using a differential evolution algorithm0The parabolic envelope objective function is constructed as follows:
Figure BDA0001301457220000212
in the formula (2-4), a, b and c are respectively parabola envelope curves h' (t) ≈ at2Coefficient of the quadratic term, coefficient of the first order term and constant, + bt + c), Am,fm,θmAmplitude, frequency and phase, respectively, of the power frequency part, B0The direct current component gc (t) is an actual data sampling point, the length (t) is a data point length of time t, and the value of M is 11;
setting the problem to be optimized as
Figure BDA0001301457220000213
(x) is a parabolic envelope objective function, then the steps of the differential evolution algorithm are described as follows:
(1) the initialization is carried out in such a way that,
inputting evolution parameters: population size m (40 ≦ m ≦ 60), chromosome length, that is, the number of objective function arguments, crossover probability C0.98, crossover factor F0.4, evolution algebra d (1 ≦ d ≦ 500), and lower bound x of N argumentsmin＝0.5·(a*、b*、c*、B0 *) And an upper bound xmax＝1.5·(a*、b*、c*、B0 *) Randomly generating an initial population matrix
Figure BDA0001301457220000221
Where each row represents an individual of the population and each column represents the gene of that individual. Each element of the initial population matrix is generated as follows:
xmn＝xmin(n)+rand(0,1)·(xmax(n)-xmin(n))，
in the above formula, rand (0,1) is a random number generated between (0, 1).
(2) The variation is carried out on the basis of the variation,
for each individual x in the populationmnGenerating three random integers r1,r2,r3∈{1,2,…,N},r1≠r2≠r3And a random integer jrandE.g. 1,2, …, N, generating variant individual zmn：
Figure BDA0001301457220000222
(3) The cross-over is carried out,
current individual xmnAnd variant individuals zmnCross to obtain competitive individual umn：
Figure BDA0001301457220000223
(4) The selection of the one or more of the components,
calculating competitive individuals umnTarget value f (u)mn) To obtain a selected individual kmn：
Figure BDA0001301457220000224
(5) The verification is terminated and the verification is terminated,
if it is notf(kmn) D is not more than 0.1or 500, k is outputmnAs the optimal solution. Otherwise, put xmn＝kmnAnd d +1, and turning to the mutation step (2).
The accurate parameter values for calculating the exponential envelope part and the direct current part are as follows:
approximation of a parameter based on the envelope part*、b*、c*、B0 *Calculating the range of iteration initial value, and identifying the parameters a, B, c and B of the envelope part by using a differential evolution algorithm0The parabolic envelope objective function is constructed as follows:
Figure BDA0001301457220000231
in the formula (3-4), a, b and c are respectively exponential envelope curves h' (t) ≈ aebt+ c) amplification factor, attenuation factor and constant, Am,fm,θmAmplitude, frequency and phase, respectively, of the power frequency part, B0The direct current component gc (t) is an actual data sampling point, the length (t) is a data point length of time t, and the value of M is 11;
setting the problem to be optimized as
Figure BDA0001301457220000232
(x) is an exponential envelope objective function, then the steps of the differential evolution algorithm are described as follows:
(1) the initialization is carried out in such a way that,
inputting evolution parameters: population size m (40 ≦ m ≦ 60), chromosome length, that is, the number of objective function arguments, crossover probability C0.98, crossover factor F0.4, evolution algebra d (1 ≦ d ≦ 500), and lower bound x of N argumentsmin＝0.5·(a*、b*、c*、B0 *) And an upper bound xmax＝1.5·(a*、b*、c*、B0 *) Randomly generating an initial population matrix
Figure BDA0001301457220000233
Wherein each rowRepresents an individual of the population, each column representing the gene of that individual. Each element of the initial population matrix is generated as follows:
xmn＝xmin(n)+rand(0,1)·(xmax(n)-xmin(n))，
in the above formula, rand (0,1) is a random number generated between (0, 1).
(2) The variation is carried out on the basis of the variation,
for each individual x in the populationmnGenerating three random integers r1,r2,r3∈{1,2,…,N},r1≠r2≠r3And a random integer jrandE.g. 1,2, …, N, generating variant individual zmn：
Figure BDA0001301457220000241
(3) The cross-over is carried out,
current individual xmnAnd variant individuals zmnCross to obtain competitive individual umn：
Figure BDA0001301457220000242
(4) The selection of the one or more of the components,
calculating competitive individuals umnTarget value f (u)mn) To obtain a selected individual kmn：
Figure BDA0001301457220000243
(5) The verification is terminated and the verification is terminated,
if f (k)mn) D is not more than 0.1or 500, k is outputmnAs the optimal solution. Otherwise, put xmn＝kmnAnd d +1, and turning to the mutation step (2).
According to the embodiment of the invention, by inputting sampling data gc (t), Matlab is used for searching curve envelope points, and characteristic quantities such as envelope point slope, second-order derivative value and the like are used for judging the type of a dynamic signal so as to determine currentThe mathematical model of (1). The embodiment of the invention can select the envelope parameter pre-estimation algorithm according to the determined mathematical model, and firstly estimates the harmonic parameter A of the power frequency part by using a Hanning window interpolation methodm,fm,θm. The embodiment of the invention searches the envelope points of the curve aiming at the oblique line envelope, the exponential envelope and the parabolic envelope, and estimates the envelope parameters by using respective estimation algorithm to obtain an approximate value a*、b*、c*、B0 *. And using the approximation a*、b*、c*、B0 *The iterative initial value range (50% up-down fluctuation of the estimated value) of the differential evolution algorithm is calculated, and the target function is the root mean square error value (RMSE) of the estimated value g (t) and the sampling value gc (t). The embodiment of the invention utilizes a differential evolution algorithm to identify a, B, c and B of the envelope part0And (6) obtaining accurate results according to the parameters.
Embodiments of the invention are further illustrated below:
the invention is explained by taking modeling analysis of an electric locomotive of a certain traction station as an example, wherein the sampling frequency of a waveform recording device is 5000Hz, 2 to 3 groups are sampled, each group is different for 1 to 5min, the voltage and the current are synchronously collected, and the collected current curve of the electric locomotive is shown as figure 2. In fig. 2, the 01 th section is a parabolic envelope model, the 02 th section is a diagonal envelope model, and the 03 th section is an exponential envelope model.
The slope envelope model is described below, in which the harmonic order is M-11, and the relative Root Mean Square (RMSE) error of 11 harmonic analysis is 0.023.
The diagonal envelope model converges in the objective function when the differential evolution algorithm of the embodiment of the invention is used for iteration to the 30 th step, and the final Root Mean Square Error (RMSE) is 0.087. Substituting the final parameter iteration result into a diagonal envelope model:
Figure BDA0001301457220000251
the plotted curve is compared to the original curve, for example as shown in fig. 3, and it can be seen that the plotted curve substantially approximates the original signal curve. As shown in a graph of fig. 3, which plots a curve and an original curve, the method for identifying dynamic signal parameters provided by the embodiment of the present invention can achieve higher accuracy and better effect. The embodiment of the invention can be applied to power grid harmonic analysis, electric energy metering and electric energy quality monitoring.
The embodiment of the invention provides a more perfect mathematical model for describing the dynamic signal current, and has better applicability; organically combining a windowing interpolation algorithm and an envelope parameter estimation algorithm, and solving envelope part parameters a, B and c and a direct current part component B in the model by using the envelope parameter estimation algorithm0The limitation of the application of the windowing interpolation algorithm is overcome. The embodiment of the invention shows that the following dynamic signal actual measurement calculation results: the method has a good effect on global optimization of the envelope parameters by adopting the differential evolution algorithm, avoids the limitation of a common optimization algorithm, and has higher convergence speed and higher precision.
FIG. 4 is a block diagram of a dynamic signal parameter identification system according to an embodiment of the present invention. As shown in fig. 4, a dynamic signal parameter identification system 400 includes:
the establishing unit 401 is configured to establish a mathematical model of the current according to the shape of the envelope curve of the dynamic signal current waveform.
An initialization unit 402, which determines the type of the mathematical model of the current according to the first derivative value, the second derivative value, and the ratio of the second derivative value to the first derivative value of the curve envelope point.
A first calculating unit 403, where the first calculating unit 403 selects a pre-estimation algorithm for the determined mathematical model type of the current according to the determined mathematical model type of the current, and pre-estimates parameters of an envelope part and a direct current part by using the pre-estimation algorithm to obtain approximate values of the parameters of the envelope part and the direct current part;
a second calculating unit 404, where the second calculating unit 404 identifies the envelope parameter by using a difference algorithm according to the approximate value of the envelope parameter, and obtains an accurate value of the envelope parameter and an accurate value of the dc component.
The dynamic signal parameter identification system 400 according to the embodiment of the present invention corresponds to the dynamic signal parameter identification method 100 according to another embodiment of the present invention, and is not described herein again.
The invention has been described with reference to a few embodiments. However, other embodiments of the invention than the one disclosed above are equally possible within the scope of the invention, as would be apparent to a person skilled in the art from the appended patent claims.
Generally, all terms used in the claims are to be interpreted according to their ordinary meaning in the technical field, unless explicitly defined otherwise herein. All references to "a/an/the [ device, component, etc ]" are to be interpreted openly as referring to at least one instance of said device, component, etc., unless explicitly stated otherwise. The steps of any method disclosed herein do not have to be performed in the exact order disclosed, unless explicitly stated.

Claims (12)

1. A method of dynamic signal parameter identification, the method comprising:
establishing a mathematical model of the current according to the shape of the envelope curve of the dynamic signal current waveform; estimating harmonic parameters of a power frequency part by using a Hanning window Hanning interpolation method;
judging the type of a mathematical model of the current according to the first derivative value and the second derivative value of the curve envelope point and the ratio of the second derivative value to the first derivative value; the type of the mathematical model of the current is judged according to the first derivative value, the second derivative value and the ratio of the second derivative value to the first derivative value of the curve envelope point,
the mathematical model of the oblique line envelope curve is h (t) approximately equal to (at + b) (1-1),
in the formula (1-1), a and b are respectively a slope and a constant of a sloping envelope curve h (t) (at + b), and t is a sampling time corresponding to the dynamic signal;
calculating the slope of the curve envelope point:
Figure FDA0002623312550000011
in the formula (1-2), Δ t is any time interval, and t1 is any time in the sampling time period;
if the calculated slope value of the envelope point of the envelope curve is a constant, judging that the type of the mathematical model of the current is a sloping line envelope model;
selecting a pre-estimation algorithm aiming at the judged mathematical model type of the current according to the judged mathematical model type of the current, and pre-estimating parameters of an envelope part and a direct current part by using the pre-estimation algorithm to obtain approximate values of the parameters of the envelope part and the direct current part;
and identifying the envelope parameters by using a differential algorithm according to the approximate values of the envelope parameters to obtain accurate values of the envelope parameters and the direct current components.
2. The method of claim 1, wherein the mathematical model types are a sloped envelope model, a parabolic envelope model, and an exponential envelope model, respectively.
3. The method of claim 1, wherein the step of establishing the oblique line envelope model according to the harmonic parameters of the power frequency part comprises the following steps:
Figure FDA0002623312550000021
in the formula (1), a and b are respectively the slope and constant of the oblique line envelope curve h (t) (at + b), Am，fm,θmRespectively, power frequency partial amplitude, power frequency partial frequency and power frequency partial phase, B0The value of M is 11, and t is the sampling time corresponding to the dynamic signal;
the parabolic envelope model is:
Figure FDA0002623312550000022
in the formula (2), a, b and c are respectively parabola envelope curves h' (t) ≈ at2Coefficient of the quadratic term, coefficient of the first order term and constant, + bt + c), Am,fm,θmRespectively, power frequency partial amplitude, power frequency partial frequency and power frequency partial phase, B0The value of M is 11, and t is the sampling time corresponding to the dynamic signal;
the exponential envelope model is:
Figure FDA0002623312550000023
in the formula (3), a, b and c are respectively exponential envelope curves h' (t) ≈ aebt+ c) amplification factor, attenuation factor and constant, Am,fm,θmRespectively, power frequency partial amplitude, power frequency partial frequency and power frequency partial phase, B0The value of M is 11, and t is the sampling time corresponding to the dynamic signal.
4. The method of claim 1, wherein determining a mathematical model type of a current based on a first derivative value, a second derivative value, and a ratio of the second derivative value to the first derivative value of the curve envelope point comprises,
the mathematical model of the parabola envelope curve is h' (t) ≈ at2+bt+c) (2-1)，
In the formula (2-1), a, b and c are respectively parabola envelope curves h' (t) ≈ at2A quadratic term coefficient, a primary term coefficient and a constant of + bt + c), wherein t is the sampling time corresponding to the dynamic signal;
calculating a second order differential function value of a curve envelope point:
Figure FDA0002623312550000031
in the formula (2-2), Δ t is any time interval, and t1 is any time within the sampling period;
and if the calculated second order differential function value of the envelope point of the envelope curve is constant, judging that the type of the mathematical model of the current is a parabolic envelope model.
5. The method of claim 1, wherein determining a mathematical model type of a current based on a first derivative value, a second derivative value, and a ratio of the second derivative value to the first derivative value of the curve envelope point comprises,
the mathematical model of the exponential envelope curve is h' (t) ≈ aebt+c) (3-1)，
In the formula (3-1), a, b and c are respectively exponential envelope curves h' (t) ≈ aebt+ c) amplification factor, attenuation factor and constant;
calculating the ratio of the second order differential to the first order differential of the envelope point:
Figure FDA0002623312550000032
Figure FDA0002623312550000041
in the formula (3-2), Δ t is any time interval, t1Is any time in the sampling period;
and if the ratio of the second derivative value of the curve enveloping point to the first derivative value of the enveloping point is constant, judging that the type of the mathematical model of the current is an exponential enveloping model.
6. The method according to claim 1, wherein a prediction algorithm for the determined mathematical model type of the current is selected according to the determined mathematical model type of the current, and parameters of an envelope part and a direct current part are predicted by using the prediction algorithm to obtain approximate values of the parameters of the envelope part and the direct current part, wherein the prediction of the parameters of the oblique line envelope part and the direct current part is as follows:
according to the selected sampling timeDividing the sampling data points into time segments at intervals delta t, screening out maximum values in each time segment range to obtain envelope points of the curve in the whole sampling time range, calculating first derivatives of oblique line functions of the envelope part, and estimating a, B and B0Approximation a of*、b*、B0 *Let the envelope curve be h (T) approximately equal to (at + b), T be the power frequency period, T1For any time within the sampling period, the set of equations is calculated as follows:
(1)
Figure FDA0002623312550000042
(2)
Figure FDA0002623312550000043
(3)
Figure FDA0002623312550000044
in the formula sets (1-3), a and B are respectively the slope and constant of the oblique line envelope curve h (t) (at + B), and B0Is a direct current component; a is*、b*、B0 *Is a, B, B0An approximation of (d); Δ t is any time interval, t1Is any time in the sampling period; length (T) is the length of the data point at time T, and T is length (T).
7. The method according to claim 1, wherein a prediction algorithm for the determined mathematical model type of the current is selected according to the determined mathematical model type of the current, and parameters of an envelope part and a direct current part are predicted by using the prediction algorithm to obtain approximate values of the parameters of the envelope part and the direct current part, wherein the prediction of the parameters of the envelope part and the direct current part is as follows:
dividing the sampling data point into time segments according to the selected sampling time interval delta t, and then screening out the maximum value in each time segment range, thereby obtaining the curve in the whole sampling time rangeEnvelope point, calculating the second derivative of the parabolic function of envelope part, and estimating a, B, c and B0Approximation a of*、b*、c*、B0 *Let the envelope curve be h' (t) ≈ at2+ bt + c), T is power frequency period, T1At any time in the sampling period, the calculation formula group is as follows:
(1)
Figure FDA0002623312550000051
(2)
Figure FDA0002623312550000052
(3)
Figure FDA0002623312550000053
(4)
Figure FDA0002623312550000054
(2-3)，
in the formula sets (2-3), a, b and c are respectively parabola envelope curves h' (t) ≈ at2Coefficient of quadratic term, coefficient of primary term and constant, + bt + c), B0Is a direct current component; a is*、b*、c*、B0 *Is a, B, c, B0Is any time interval, t1Is any time in the sampling period; length (T) is the length of the data point at time T, and T is length (T).
8. The method according to claim 1, wherein a prediction algorithm for the determined mathematical model type of the current is selected according to the determined mathematical model type of the current, and parameters of an envelope part and a direct current part are predicted by using the prediction algorithm to obtain approximate values of the parameters of the envelope part and the direct current part, wherein the prediction of the parameters of the exponential envelope part and the direct current part is as follows:
according to the selectionDividing sampling data points into time segments by sampling time intervals delta t, screening out maximum values in each time segment range to obtain envelope points of a curve in the whole sampling time range, calculating the ratio of a second derivative of an exponential function of the envelope part to the first-order layer number, and calculating a, B, c and B0Approximation a of*、b*、c*、B0 *Let the envelope curve be h' (t) ≈ aebt+ c), T is the power frequency period, T1For any time within the sampling period, the set of equations is calculated as follows:
(1)
Figure FDA0002623312550000061
(2)
Figure FDA0002623312550000062
(3)
Figure FDA0002623312550000063
(4)
Figure FDA0002623312550000064
(3-3)，
in the formula group (3-3), a, b and c are respectively exponential envelope curves h' (t) ≈ aebt+ c) amplification factor, attenuation factor and constant, B0Is a direct current component; a is*、b*、c*、B0 *Is a, B, c, B0An estimate of (d); Δ t is any time interval, t1Is any time in the sampling period; length (T) is the length of the data point at time T, and T is length (T).
9. The method according to claim 6, wherein the envelope parameters are identified by a difference algorithm according to the approximate value of the envelope parameters, and accurate values of the envelope parameters and the direct current component are obtained, wherein the accurate values of the parameters of the oblique line envelope part and the direct current part are calculated as follows:
according to a parameter approximation a of the envelope part*、b*、c*、B0 *Calculating the range of iteration initial value, and identifying the parameters a, B, c and B of the envelope part by using a differential evolution algorithm0The formula of the target function of the oblique line envelope is constructed as follows:
Figure FDA0002623312550000071
in the formulas (1-4), a and b are respectively the slope and constant of the oblique line envelope curve h (t) (at + b), Am,fm,θmAmplitude, frequency and phase, respectively, of the power frequency part, B0Is a direct current component, gc (t) is an actual data sampling point, length (t) is a data point length of time t, and the value of M is 11;
setting the problem to be optimized as
Figure FDA0002623312550000072
(x) is the target function of the slope envelope, the steps of the differential evolution algorithm are described as follows:
(1) the initialization is carried out in such a way that,
inputting evolution parameters: population size m (40 ≦ m ≦ 60), chromosome length, that is, the number of objective function arguments, crossover probability C0.98, crossover factor F0.4, evolution algebra d (1 ≦ d ≦ 500), and lower bound for N arguments
Figure FDA0002623312550000081
And upper bound
Figure FDA0002623312550000082
Randomly generating an initial population matrix
Figure FDA0002623312550000083
Wherein each row represents an individual of the population, each column represents a gene of the individual, each element of the initial population matrixGenerated in the following way:
Figure FDA0002623312550000086
in the above formula, rand (0,1) is a random number generated between (0, 1);
(2) the variation is carried out on the basis of the variation,
for each individual x in the populationmnGenerating three random integers r1，r2，r3∈{1，2，…，N}，r1≠r2≠r3And a random integer jrandE.g. 1,2, …, N, generating variant individual Zmn：
Figure FDA0002623312550000084
(3) The cross-over is carried out,
current individual xmnAnd variant individuals zmnCross to obtain competitive individual umn：
Figure FDA0002623312550000085
(4) Selecting
Calculating competitive individuals umnTarget value f (u)mn) To obtain a selected individual kmn：
Figure FDA0002623312550000091
(5) The verification is terminated and the verification is terminated,
if f (k)mn) D is not more than 0.1or 500, k is outputmnAs the optimal solution, otherwise, setting xmn＝kmnAnd d +1, and turning to the mutation step (2).
10. The method according to claim 7, wherein the envelope parameters are identified by using a difference algorithm according to the approximate value of the envelope parameters, and accurate values of the envelope parameters and the direct current component are obtained, wherein the accurate values of the parameters of the parabolic envelope part and the direct current part are calculated as follows:
according to a parameter approximation a of the envelope part*、b*、c*、B0 *Calculating the range of iteration initial value, and identifying the parameters a, B, c and B of the envelope part by using a differential evolution algorithm0The formula of the parabolic envelope objective function is constructed as follows:
Figure FDA0002623312550000092
in the formula (2-4), a, b and c are respectively parabola envelope curves h' (t) ≈ at2Coefficient of the quadratic term, coefficient of the first order term and constant, + bt + c), Am,fm,θmAmplitude, frequency and phase, respectively, of the power frequency part, B0The direct current component gc (t) is an actual data sampling point, the length (t) is a data point length of time t, and the value of M is 11;
setting the problem to be optimized as
Figure FDA0002623312550000101
(x) is a parabolic envelope objective function, then the steps of the differential evolution algorithm are described as follows:
(1) the initialization is carried out in such a way that,
inputting evolution parameters: population size m (40 ≦ m ≦ 60), chromosome length, that is, the number of objective function arguments, crossover probability C0.98, crossover factor F0.4, evolution algebra d (1 ≦ d ≦ 500), and lower bound for N arguments
Figure FDA0002623312550000102
And upper bound
Figure FDA0002623312550000103
Randomly generating an initial population matrix
Figure FDA0002623312550000104
Wherein each row represents an individual of the population and each column represents a gene of this individual, the elements of the initial population matrix are generated in the following manner:
Figure FDA0002623312550000105
in the above formula, rand (0,1) is a random number generated between (0, 1);
(2) the variation is carried out on the basis of the variation,
for each individual x in the populationmnGenerating three random integers r1,r2,r3∈{1,2,…,N},r1≠r2≠r3And a random integer jrandE.g. 1,2, …, N, generating variant individual Zmn：
Figure FDA0002623312550000106
(3) The cross-over is carried out,
current individual xmnAnd variant individuals zmnCross to obtain competitive individual umn：
Figure FDA0002623312550000111
(4) Selecting
Calculating competitive individuals umnTarget value f (u)mn) To obtain a selected individual kmn：
Figure FDA0002623312550000112
(5) The verification is terminated and the verification is terminated,
if f (k)mn) D is not more than 0.1or 500, k is outputmnAs the optimal solution, otherwise, setting xmn＝kmnAnd d +1, and turning to the mutation step (2).
11. The method according to claim 8, wherein the envelope parameters are identified by a difference algorithm according to the approximate value of the envelope parameters, and accurate values of the envelope parameters and the dc component are obtained, wherein the accurate values of the parameters of the exponential envelope part and the dc part are calculated as follows:
according to a parameter approximation a of the envelope part*、b*、c*、B0 *Calculating the range of iteration initial value, and identifying the parameters a, B, c and B of the envelope part by using a differential evolution algorithm0The formula of the parabolic envelope objective function is constructed as follows:
Figure FDA0002623312550000113
in the formula (3-4), a, b and c are respectively exponential envelope curves h' (t) ≈ aebt+ c) amplification factor, attenuation factor and constant, Am,fm,θmAmplitude, frequency and phase, respectively, of the power frequency part, B0The direct current component gc (t) is an actual data sampling point, the length (t) is a data point length of time t, and the value of M is 11;
setting the problem to be optimized as
Figure FDA0002623312550000121
(x) is an exponential envelope objective function, then the steps of the differential evolution algorithm are described as follows:
(1) the initialization is carried out in such a way that,
inputting evolution parameters: population size m (40 ≦ m ≦ 60), chromosome length, that is, the number of objective function arguments, crossover probability C0.98, crossover factor F0.4, evolution algebra d (1 ≦ d ≦ 500), and lower bound for N arguments
Figure FDA0002623312550000122
And upper bound
Figure FDA0002623312550000123
Randomly generating an initial population matrix
Figure FDA0002623312550000124
Wherein each row represents an individual of the population and each column represents a gene of this individual, the elements of the initial population matrix are generated in the following manner:
Figure FDA0002623312550000125
in the above formula, rand (0,1) is a random number generated between (0, 1);
(2) the variation is carried out on the basis of the variation,
for each individual x in the populationmnGenerating three random integers r1,r2,r3∈{1,2，…,N},r1≠r2≠r3And a random integer jrandE.g. 1,2, …, N, generating variant individual Zmn：
Figure FDA0002623312550000126
(3) The cross-over is carried out,
current individual xmnAnd variant individuals zmnCross to obtain competitive individual umn：
Figure FDA0002623312550000131
(4) Selecting
Calculating competitive individuals umnTarget value f (u)mn) To obtain a selected individual kmn：
Figure FDA0002623312550000132
(5) The verification is terminated and the verification is terminated,
if f (k)mn) D is not more than 0.1or 500, k is outputmnAs the optimal solution, otherwise, setting xmn＝kmnAnd d +1, and turning to the mutation step (2).
12. A dynamic signal parameter identification system, the system comprising:
the establishing unit is used for establishing a mathematical model of the current according to the envelope curve shape of the dynamic signal current waveform; estimating harmonic parameters of a power frequency part by using a Hanning window Hanning interpolation method;
the initial unit judges the type of a mathematical model of the current according to the first order derivative value and the second order derivative value of the curve envelope point and the ratio of the second order derivative value to the first order derivative value; the type of the mathematical model of the current is judged according to the first derivative value, the second derivative value and the ratio of the second derivative value to the first derivative value of the curve envelope point,
the mathematical model of the oblique line envelope curve is h (t) approximately equal to (at + b) (1-1),
in the formula (1-1), a and b are respectively a slope and a constant of a sloping envelope curve h (t) (at + b), and t is a sampling time corresponding to the dynamic signal;
calculating the slope of the curve envelope point:
Figure FDA0002623312550000133
in the formula (1-2), Δ t is any time interval, and t1 is any time in the sampling time period;
if the calculated slope value of the envelope point of the envelope curve is a constant, judging that the type of the mathematical model of the current is a sloping line envelope model;
the first calculation unit selects a pre-estimation algorithm aiming at the judged mathematical model type of the current according to the judged mathematical model type of the current, and pre-estimates the parameters of the envelope part and the direct current part by utilizing the pre-estimation algorithm to obtain approximate values of the parameters of the envelope part and the direct current part;
and the second calculating unit identifies the envelope parameters by using a differential algorithm according to the approximate values of the envelope parameters to obtain accurate values of the envelope parameters and the direct current components.
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